最终版:)
Introduction
As we all know, Frisbee is a very important sport for Moonshot. But our school does not have a playground in the true sense, so everyone hopes to play frisbee in our school. At Moonshot, the most suitable place to play Frisbee is the rooftop.
We asked a lot of community members about this.
From Ryan, he thinks it depends on the potential safety hazards of the roof
Jason also mentioned the possibility of a Frisbee being thrown and injuring someone
Ellie didn’t think we could either, because the Frisbee would be thrown
In addition to raising our questions, we also raised a number of reasons, namely that the roof surface is not smooth and we have not established our own safety philosophy
Only Ziwen, she thinks we can unless we’re going to throw it over the fence.
From the above comments, most people do not support playing Frisbee on the rooftop. That is why they all have such thoughts?
Problem interpretation
So can we play Frisbee on the top of the building？
There are several specific aspects to sum up:
1. Throwing objects at high altitude is not safe
It would be too dangerous if it hurts a passing pedestrian.
2. The rooftop facilities are not perfect
Our fence is not that strong, and the weight of the flying disc and the speed of the learner’s movement may damage it.
The ground of the rooftop is not very smooth, and people may get their feet injured and injured if they exercise on it.
3. Learners can’t manage well
In the video of the opening ceremony of the Frisbee Cup, some learners hit the wall with a Frisbee.
When people play Frisbee in school, they always throw it in various places.
Smash the glass with a frisbee outside our school
4. How high are the building and the fence respectively?
5. What’s the average speed and the average mass of frisbee?
For these questions above, we can search that how to form high-altitude parabola, or how likely is it to be?
After our panel discussion, we concluded that as long as there is a high-altitude parabola is dangerous and not allowed. So the question that can be studied is that people can’t play Frisbee on the roof as long as it’s thrown out of the roof.
We’ll look at this in two parts:
The height of the platform fence and the height of the highest point of the parabola corresponding to the Frisbee
If the height of the highest point is greater than the height of the fence, it is possible to fly out again during normal movement.
Assumptions
Before testing, we made some reasonable assumptions.
1) Assuming that the fence and the ground are at a right angle of 90 degrees
(This means that we can use the existing knowledge of trigonometric functions to measure these data)
2) Assume that all those who go to the rooftop to play Frisbee have no intention of throwing the Frisbee downstairs.
3) The protractor is perpendicular to the ground and the rope used for measurement is a straight line
4) As long as the height of the highest point of the frisbee is greater than the height of the roof fence, it can indicate that it is a high-altitude parabolic.
Measuring
Fence height
We decided to measure the height by using trigonometry, using a rope measuring the two angles (one to the top of the fence, the other to the bottom), and with the knowing of how far we are with the wall, we can measure the height of the fence/building.
But before measuring and calculating, we need to make a protractor first.
We got a rectangular piece of paper. It is known that all four corners are 90 degrees.
We folded one corner of the paper for times, which is an equal angle of 4*2=8.
Use the given tool (compass) to make, first take a length on the two sides of the 45 degree angle, and then use this length as the radius to draw length in the middle. The two lengths converge to form an intersection, and a ray is formed from the vertex of the corner and that intersection.
The angle between this ray and the edge is the new angle. By analogy, we can reach the angle of 11.25 degrees.
90/8=11.25.
That is to say, the angle of each small angle as shown in the figure below is 11.25 degrees. Add and subtract these 11.25 degree angles, and we can get many angles.
With the protractor, the next step is to measure the height of the fence and building. (Problem statistics article 4)
We marked the distance on the ground. Pull a straight line from the fixed point and aim your eyes at the height of the building and the position of the fence vertices.
The first time was the distance between the fixed point and the building of 4.5 meters, the angle between the ground and the top of the building was 68 degrees, and the angle with the top of the fence was 74 degrees.
The 74-degree angle is observed by the naked eye, because in the angler we made, the angle between the ground and the slash connecting the two points was close to 78.5 degrees.
(11.25\times7=78.5 degrees)
At 5.5 meters, the angle between the ground and the top of the building is 66 degrees and 71 degrees from the top of the fence.
(and so on)
At 7.5 meters, the angle with the bottom is 57 degrees and the angle with the top angle is 62 degrees.
At 9 meters, the angle with the bottom is 52 degrees and the angle with the top angle is 59 degrees.
Frisbee height
2/3x=1.75m
x=21/8
1/3x=0.875m
altogether 1.75+0.875=2.625m≈2.63
Assuming that the ratio of the height of the flying disc to the height of the person is 5:4,
4x=1.80
x=0.45m
5x=2.25m
Assuming that the height of the person jumping up is 1.90m, the ratio of the height of the flying disc to the height of the person is estimated to be 5:3.
3x=1.9
x=0.63
5x=3.15m
The height of this person is changed to 1.85
Assuming that the height of the person jumping up is 1.85m, the ratio of the height of the flying disc to the height of the person is estimated to be 5:4.
4x=1.85
x≈0.46
5x=2.31m
取平均：\frac{2.63+2.25+3.15+2.31}{4}=2.59m
because 2.59<3.57
so most of the time the highest point of the Frisbee is not as high as the fence
Conclusion
This is the situation where the Frisbee is thrown out of the lightest highest point. In other words, even if it is thrown lightly, the frisbee will fly to a height of 2.5 or more. It is very easy to fly out.
Furthermore, there are too many dangerous accidents that might happened if the frisbees fly out of the fence. So that we can know the fence is not tall enough for avoiding the dangerous accidents by through the frisbee out.
Just like Figure 7, the calculated height is 3.15 meters, so there is a risk of being thrown out of the roof.
According to the problem interpretation, as long as the frisbee has a chance of being thrown out of the rooftop, it is unrealistic to play frisbee on the rooftop.
Errors&Weaknesses
1) Our tools have many limitations.
The line is not necessarily completely straight, and the angle of the “measuring angler” is not necessarily a complete right angle.
2) Due to paper and drawing tools limitations, we cannot accurately calculate each degree when making a scaler, resulting in errors.
(Our tool only has round gauges and scaleless rulers)
3) Assumptions may not be established, such as uneven ground or building is not vertical.
4) At that time when measuring data, we could not go up to the roof to put a line down, not so long line. Viewing with your eyes can produce errors.
5) My height estimate is not accurate enough. In fact, I could measure the height of a few more landmark buildings at that time, so as to reduce the error caused by visual observation.
Summary
According to all above, our conclusion is we can’t play frisbee on the rooftop, it is very easy for the frisbee to fall from the rooftop, it will cause safety accidents.